Neuron models of the generic bifurcation type:network analysis and data modeling

Minimal nonlinear dynamic neuron models of the generic bifurcation type may provide the middle way between the detailed models favored by experimentalists and the simplified threshold and rate model of computational neuroscientists. This thesis investigates to which extent generic bifurcation type models grasp the essential dynamical features that may turn out play a role in cooperative neural behavior. The thesis considers two neuron models, of increasing complexity, and one model of synaptic interactions. The FitzHugh-Nagumo model is a simple two-dimensional model capable only of spiking behavior, and the Hindmarsh-Rose model is a three-dimensional model capable of more complex dynamics such as bursting and chaos. The model for synaptic interactions is a memory-less nonlinear function, known as fast threshold modulation (FTM). By means of a combination of nonlinear system theory and bifurcation analysis the dynamical features of the two models are extracted. The most important feature of the FitzHugh-Nagumo model is its dynamic threshold: the spike threshold does not only depend on the absolute value, but also on the amplitude of changes in the membrane potential. Part of the very complex, intriguing bifurcation structure of the Hindmarsh-Rose model is revealed. By considering basic networks of FTM-coupled FitzHugh-Nagumo (spiking) or Hindmarsh-Rose (bursting) neurons, two main cooperative phenomena, synchronization and coincidence detections, are addressed. In both cases it is illustrated that pulse coupling in combination with the intrinsic dynamics of the models provides robustness. In large scale networks of FTM-coupled bursting neurons, the stability of complete synchrony is independent from the network topology and depends only on the number of inputs to each neuron. The analytical results are obtained under very restrictive and biologically implausible hypotheses, but simulations show that the theoretical predictions hold in more realistic cases as well. Finally, the realism of the models is put to a test by identification of their parameters from in vitro measurements. The identification problem is addressed by resorting to standard techniques combined with heuristics based on the results of the reported mathematical analysis and on a priori knowledge from neuroscience. The FitzHugh-Nagumo model is only able to model pyramidal neurons and even then performs worse than simple threshold models; it should be used only when the advantages of the more realistic threshold mechanism are prevalent. The Hindmarsh-Rose model can model much of the diversity of neocortical neurons; it can be used as a model in the study of heterogeneous networks and as a realistic model of a pyramidal neuron

A computational study of sleep and the hemispheres of the brain

Sleep and sleep cycles have been studied for over a century, and scientists have worked on modeling sleep for nearly as long as computers have existed. Despite this extensive study, sleep still holds many mysteries. Larger and more extensive sleep-wake models have been developed, and the circadian drive has been depicted in numerous fashions, as well as incorporated into scores of studies. With the ever-growing knowledge of sleep comes the need to find more ways to examine, quantify, and define it in the context of the most complex part of the human anatomy -- the brain. Presented here is the development of a computational model that explores the activity of individual neurons, modeled with coupled nonlinear ordinary differential equations, in key sleep-related brain regions. The activity patterns of the individual neurons are studied, as well as their synchronization with other neurons within the same region. The model is expanded into two separate interacting hemispheres, whose activity and synchronization reveal chimera-like activity. Multiple different perspectives on jetlag are presented, exploring the impact of circadian rhythm changes. Unihemispheric sleep, the unusual form of sleep exhibited by some ocean creatures and species of birds, is observed, as well as asymmetric sleep, which occurs in human subjects suffering from sleep apnea. These investigations provide a new perspective on the intricate balance between the neural activity in different brain regions that drives the essential phenomenon that is sleep --Abstract, page iii

A Computational Study of Sleep and the Hemispheres of the Brain

Sleep and sleep cycles have been studied for over a century, and scientists have worked on modeling sleep for nearly as long as computers have existed. Despite this extensive study, sleep still holds many mysteries. Larger and more extensive sleep-wake models have been developed, and the circadian drive has been depicted in numerous fashions, as well as incorporated into scores of studies. With the ever-growing knowledge of sleep comes the need to find more ways to examine, quantify, and define it in the context of the most complex part of the human anatomy – the brain. Presented here is the development of a computational model that explores the activity of individual neurons, modeled with coupled nonlinear ordinary differential equations, in key sleep-related brain regions. The activity patterns of the individual neurons are studied, as well as their synchronization with other neurons within the same region. The model is expanded into two separate interacting hemispheres, whose activity and synchronization reveal chimera-like activity. Multiple different perspectives on jetlag are presented, exploring the impact of circadian rhythm changes. Unihemispheric sleep, the unusual form of sleep exhibited by some ocean creatures and species of birds, is observed, as well as asymmetric sleep, which occurs in human subjects suffering from sleep apnea. These investigations provide a new perspective on the intricate balance between the neural activity in different brain regions that drives the essential phenomenon that is sleep

Modellierung und Analyse des Thalamokortischen Systems

Physiological evidence localizes the thalamocortical system as the functional unit being responsible for the perception of sensory input. In this thesis the dynamical processes in the thalamus during sleep are reduced to their bare bones. For this purpose the dynamical behavior of conductance based neuron models, which describe biophysical details with high accuracy, is investigated and reduced models of this behavior are derived. The simplified models derived in this thesis allow an explanation of how sensory perception is strongly decreased during sleep within the framework of nonlinear dynamics. A minimal model for such a mechanism is derived, coarse graining out details but preserving most salient dynamical features. If several of these models are coupled in a network the experimental observed influence of cortical slow-wave oscillations on thalamic spindle oscillations during deep sleep can be reproduced. In particular the influence of cortical oscillations on the synchrony in a thalamic network is studied and the underlying control mechanism is uncovered, leading to a control method which might be applicable for several types of oscillations in the central nervous system.Physiologisch betrachtet ist das thalamokortische System für die Verarbeitung und Wahrnehmung von sensorischen Reizen zuständig. In dieser Arbeit werden die dynamischen Vorgänge im Thalamus während des Schlafes auf ihre grundlegenden Eigenschaften reduziert. Dazu wird das dynamische Verhalten von komplexen Neuronenmodellen untersucht, die biophysikalische Details mit hoher Genauigkeit wiedergeben und vereinfachte Modelle dieses Verhaltens eingeführt. Diese vereinfachten Modelle erlauben es, mit Hilfe der nichtlinearen Dynamik den Rückgang der sensorischen Wahrnehmung im Schlaf zu erklären. Dazu wird ein minimales Modell für den zugrunde liegenden Mechanismus abgeleitet, in dem Details vernachlässigt werden, ohne dass jedoch die wichtigsten dynamischen Eigenschaften verloren gehen. Koppelt man viele dieser Modelle in einem Netzwerk, so lässt sich der experimentell beobachtete Einfluss kortikaler Oszillationen auf thalamische Oszillationen reproduzieren. Ein besonderes Augenmerk liegt dabei auf der Synchronisation der thalamischen Oszillationen und dem zugrunde liegenden Mechanismus, welcher möglicherweise auch in anderen neuronalen Systemen anwendbar ist

Mecanismos de codificación y procesamiento de información en redes basadas en firmas neuronales

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Escuela Politécnica Superior, Departamento de Tecnología Electrónica y de las Comunicaciones. Fecha de lectura: 21-02-202

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Huygens synchronization of medial septal pacemaker neurons generates hippocampal theta oscillation

Episodic learning and memory retrieval are dependent on hippocampal theta oscillation, thought to rely on the GABAergic network of the medial septum (MS). To test how this network achieves theta synchrony, we recorded MS neurons and hippocampal local field potential simultaneously in anesthetized and awake mice and rats. We show that MS pacemakers synchronize their individual rhythmicity frequencies, akin to coupled pendulum clocks as observed by Huygens. We optogenetically identified them as parvalbumin-expressing GABAergic neurons, while MS glutamatergic neurons provide tonic excitation sufficient to induce theta. In accordance, waxing and waning tonic excitation is sufficient to toggle between theta and non-theta states in a network model of single-compartment inhibitory pacemaker neurons. These results provide experimental and theoretical support to a frequency-synchronization mechanism for pacing hippocampal theta, which may serve as an inspirational prototype for synchronization processes in the central nervous system from Nematoda to Arthropoda to Chordate and Vertebrate phyla

Noise induced processes in neural systems

Real neurons, and their networks, are far too complex to be described exactly by simple deterministic equations. Any description of their dynamics must therefore incorporate noise to some degree. It is my thesis that the nervous system is organized in such a way that its performance is optimal, subject to this constraint. I further contend that neuronal dynamics may even be enhanced by noise, when compared with their deterministic counter-parts. To support my thesis I will present and analyze three case studies. I will show how noise might (i) extend the dynamic range of mammalian cold-receptors and other cells that exhibit a temperature-dependent discharge; (ii) feature in the perception of ambiguous figures such as the Necker cube; (iii) alter the discharge pattern of single cells